I'm a little confused. If "hiçbir şey" means nothing, and "… yok" means "there is not …", then wouldn't "…hiçbir şey yok" mean "there is not nothing", a double negative? Wouldn't "evde hiçbir şey var" be better? Or does Turkish grammar demand that "hiçbir şey" be paired with "yok".
There is not much logic, other than it being an extremely frequent expression. Hiç means "any", bir means "one". Funnily enough, English spells "anyone" as one word too, even though "hiçbir şey" literally translates to "any one thing", in which case it's spelt separately if I'm not mistaken.
Actually, the issue lies in that there is your preposition "at." "There is nothing at home" is a perfectly fine sentence, but it is required here.
Just going off of a theory, but I am guess you can only drop "at" when the subject is the owner of the house being mentioned. "My sisters, they are home" is fine, but you cannot say "The boxes, they are home."